Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field F across the surface S in the direction away from the origin. F = 3yi + (5 - 5x)j + (z² − 2)k - S: r(0,0)=(√5 sin cos 0)i + (√√5 sin o sin 0)j + (√5 cos $) k, 0≤ ≤π/2, 0≤0 ≤ 2π The flux of the curl of the field F across the surface S in the direction of the outward unit normal n is

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field F across
the surface S in the direction away from the origin.
F = 3yi + (5 - 5x)j + (z² − 2)k
S: r(0,0) = (√5 sin & cos 0) i + (√√5 sin þ sin 0)j + (√5 cos $) k, 0≤þ≤ñ/2, 0≤0≤2
The flux of the curl of the field F across the surface S in the direction of the outward unit normal
n is
(Type an exact answer, using as needed.)
Transcribed Image Text:Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field F across the surface S in the direction away from the origin. F = 3yi + (5 - 5x)j + (z² − 2)k S: r(0,0) = (√5 sin & cos 0) i + (√√5 sin þ sin 0)j + (√5 cos $) k, 0≤þ≤ñ/2, 0≤0≤2 The flux of the curl of the field F across the surface S in the direction of the outward unit normal n is (Type an exact answer, using as needed.)
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